Find the derivative of the function. \[ f(x)=e^{x}-x^{e} \]
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To find the derivative of the function \( f(x) = e^{x} - x^{e} \), we will apply basic differentiation rules. 1. The derivative of \( e^{x} \) is simply \( e^{x} \). 2. For the term \( x^{e} \), we can use the power rule. The derivative of \( x^{n} \) is \( n \cdot x^{n-1} \), so the derivative of \( x^{e} \) will be \( e \cdot x^{e-1} \). Putting it all together, the derivative \( f'(x) \) is: \[ f'(x) = \frac{d}{dx}(e^{x}) - \frac{d}{dx}(x^{e}) = e^{x} - e \cdot x^{e-1}. \] So, the final answer is: \[ f'(x) = e^{x} - e \cdot x^{e-1}. \]